Problem: Simplify the following expression: $\sqrt{99} + \sqrt{275}$
First, try to factor any perfect squares out of the radicals. $= \sqrt{99} + \sqrt{275}$ $= \sqrt{9 \cdot 11} + \sqrt{25 \cdot 11}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{11} + \sqrt{25} \cdot \sqrt{11}$ $= 3\sqrt{11} + 5\sqrt{11}$ Finally, simplify by combining the terms. $= ( 3 + 5 )\sqrt{11} = 8\sqrt{11}$